transformations replaced by symmetry
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8 matching pages ♦
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8 matching pages
1: 19.15 Advantages of Symmetry
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►Symmetry in of , , and
replaces the five transformations (19.7.2), (19.7.4)–(19.7.7) of Legendre’s integrals; compare (19.25.17).
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2: 19.22 Quadratic Transformations
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3: 19.25 Relations to Other Functions
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19.25.16
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4: Bille C. Carlson
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►The main theme of Carlson’s mathematical research has been to expose previously hidden permutation symmetries that can eliminate a set of transformations and thereby replace many formulas by a few.
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5: Errata
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Section 24.1
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Chapter 18 Orthogonal Polynomials
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Figure 4.3.1
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Section 27.20
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Subsection 21.10(i)
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The text “greatest common divisor of ” was replaced with “greatest common divisor of ”.
This figure was rescaled, with symmetry lines added, to make evident the symmetry due to the inverse relationship between the two functions.
Reported 2015-11-12 by James W. Pitman.
The entire Section was replaced.
The entire original content of this subsection has been replaced by a reference.
6: 18.7 Interrelations and Limit Relations
7: 20.11 Generalizations and Analogs
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►If both are positive, then allows inversion of its arguments as a modular transformation (compare (23.15.3) and (23.15.4)):
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